Overview of the study area
Shennongjia is located in the mountainous area of northwest Hubei (Fig. 1), between 109°56′-110°58′ E, 31°15′-31°57′ N, with a total area of 3215.80 km2. The southwest is dominated by mountains in the east-west direction. The highest peak of Shennongjia is 3105.40 m, which is also the highest point in central China (Xiong 2017). Shennongjia is the intersection zone of east-west flora and the transition zone of north-south flora in China. It possesses the only well-preserved subtropical forest ecosystem in the middle latitudes of the world, as well as the world’s most abundant biodiversity (Li 2017). It also constitutes a gene pool with global significance, and is widely-known as the "Green Miracle". Shennongjia comprises various ecosystems, such as forests, shrubs, meadows and wetlands, which have crucial ecological environment service functions, including climate regulation, and water and soil conservation (Peng et al. 2007).
Data sources and preprocessing treatments
This study involves 17 data indicators (Table 1). Among them, the four indicators of surface relief, slope, aspect, and water system distribution are all based on data of 2018 due to their minimal change in a short time-span. The other indicators use relevant data of 1996, 2007, and 2018.
Table 1. Description and source of evaluation indexes.
Indicator
|
Method and explanation
|
Data sources
|
Land-use types
|
125/38, 126/38 of Landsat 5 TM / Landsat 8 OLI image interpretation in 1996, 2007, 2018
Five categories: forest land, grassland,
cultivated land, construction land, and water area
|
Website of the United States Geological Survey (USGS)
(http://glovis.usgs.gov/)
|
Slope
|
Extracted from the digital elevation model (DEM)
|
Website of USGS
(http://glovis.usgs.gov/)
|
Aspect
|
Extracted from the digital elevation model (DEM)
|
Surface relief
|
Maximum elevation value - minimum elevation value in unit area
|
Vegetation coverage
|
Mixed pixel decomposing model
|
Website of USGS
(http://glovis.usgs.gov/)
|
Average annual temperature
|
Spatial interpolation combined with regression equation calculation and interpolation residuals
|
Website of the China Meteorological Administration
(http://data.cma.cn/)
|
Annual precipitation
|
Population density
|
Population / land area
|
Shennongjia Bureau of Statistics
|
Local fiscal revenue per capita
|
Local fiscal revenue / population
|
Water distribution
|
Mapping of field research and historical data
|
Shennongjia Bureau of Water Resources and Lakes
|
Surface water resources
|
Monitoring statistics
|
Quality of surface water
|
Monitoring statistics
|
Industrial wastewater discharge
|
Monitoring statistics
|
Domestic sewage discharge
|
Monitoring statistics
|
Annual tourist reception
|
According to Shennongjia tourism management report statistics
|
Shennongjia Bureau of Culture and Tourism
|
National park policy
|
Organized according to field research and data collection
|
Shennongjia National Park Administration
|
Nature reserve policy
|
The land-use data of Shennongjia is interpreted based on Landsat remote sensing images, and the spatial resolution of the images is 30 m. According to the national standard of land use status classification (GB/T 21010-2017) and the purpose of the present study, the land in Shennongjia is divided into five categories: forest land, grassland, construction land, cultivated land, and water area.
Due to the differences of data-source types and spatial accuracy of different evaluation indexes, inverse distance weighted interpolation (IDW) was used for spatial deterministic interpolation of certain statistical data with the support of the ArcGIS software platform (the raster size of spatial data was defined as 30 m × 30 m) to realize spatial localization.
Index system of ecological vulnerability assessment
In this study, the vulnerability scoring diagram (VSD) model was used. Combined with previous research results (Li and Chen 2014), through field investigation and historical data processing, the following 16 indicators were selected from three main aspects of exposure, sensitivity and adaptability, and the ecological vulnerability evaluation system of Shennongjia was constructed (Fig. 2).
Indexes of exposure can reflect the degree of which the ecosystem is affected by external disturbance or stress (Luers et al. 2003). Population density and annual tourist reception are selected to reflect the threat of population pressure on the ecosystem, and industrial wastewater discharge and residential wastewater discharge are chosen to indicate ecological vulnerability resultant from environmental pollution.
Indexes of sensitivity can reflect the response of part or the whole ecosystem to changes of the natural environment and human activities, and indicate the probability of ecological imbalance and other environmental problems in a particular region (J. Liu et al., 2015). Ecosystems with high sensitivity have a high risk of ecological problems and are the focus of restoration and protection, systems with low sensitivity are not susceptible to changes due to disturbance and are suitable for rational development. According to the actual situation of Shennongjia, climate characteristics, water environment quality, topography, vegetation status, and land use were chosen as important evaluation factors of ecological sensitivity.
Indexes of adaptability reflect the system's ability to adjust and cope with changes or disturbances of internal and external conditions, and indicate the measures and countermeasures that human beings take to deal with many ecological problems (Ren and Zhang 2016). Local fiscal revenue per capita can reflect regional economic development and, to a certain extent, it can represent the financial investment capacity of human society for ecological construction and ecological protection projects. The delimitation of nature reserves and national parks directly indicates the implementation of regional protection policies.
Index standardization
Due to the differences of dimensions, orders of magnitude and positive and negative directions of the above evaluation indexes, and in order to eliminate such possible impacts on data analysis, this study uses the range method and the hierarchical assignment method to standardize the original data of each index (Ma et al. 2015). The calculation formula is as follows (Nan et al. 2013):
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)
where Yi is the value of the ith indicator after standardized calculation, its range is 0-10, and the larger is Yi, the higher is the ecological vulnerability of the region and the more vulnerable is the ecosystem to external disturbance and damage, Xi is the original value of the ith index, Xmax is the maximum of the original value of the ith index, and Xmin is the minimum of the original value of the ith index.
As a qualitative index, land-use types need to be classified and quantified (Chen et al., 2019, Li et al., 2021). According to previous studies (Cao et al., 2021), and combined with the actual situation of Shennongjia, the standardized assignment of each land-use type was performed (Table 2).
Table 2. Standardized grading assignment of land-use types.
Land-use types
|
Forest land
|
Grassland
|
Cultivated land
|
Construction land
|
Water area
|
Assignment
|
2
|
4
|
6
|
8
|
2
|
Spatial principal component analysis
Principal component analysis (PCA) is a commonly-used multivariate statistical analysis method. This data dimension reduction algorithm is generally applied to feature extraction (Liu et al., 2015). Spatial principal component analysis (SPCA) is based on the support of the ArcGIS software platform, which extends the method of PCA to two-dimensional space (Guo et al. 2019, Li et al. 2019), so that many related complex spatial information data can be transformed into a few unrelated comprehensive indicators. The visual PCA of evaluation objects can then be completed (Wang and Dai 2018, Li et al. 2020).
Using the principal component analysis (PCA) module tool of ArcGIS, the spatial principal component analysis (SPCA) of 16 evaluation indexes in four levels is performed. Taking the cumulative contribution rate of principal components reaching more than 90% as the standard, the first six principal components (Table 3) are selected to replace the original 16 variables for analysis, in order to achieve data dimensionality reduction.
Table 3. Eigenvalue, contribution rate, and accumulated contribution rate of each principal component.
Year
|
Principal component coefficient
|
Principal component
|
|
|
PC1
|
PC2
|
PC3
|
PC4
|
PC5
|
PC6
|
1996
|
Eigenvalues λ
|
1.681
|
0.567
|
0.429
|
0.227
|
0.207
|
0.112
|
Contribution rate (%)
|
47.17
|
15.90
|
12.04
|
6.36
|
5.80
|
3.13
|
Accumulated contribution rate (%)
|
47.17
|
63.07
|
75.11
|
81.47
|
87.27
|
90.40
|
2007
|
Eigenvalues λ
|
1.864
|
0.861
|
0.435
|
0.258
|
0.186
|
0.149
|
Contribution rate (%)
|
46.13
|
21.32
|
10.77
|
6.39
|
4.61
|
3.69
|
Accumulated contribution rate (%)
|
46.13
|
67.45
|
78.22
|
84.61
|
89.22
|
92.92
|
2018
|
Eigenvalues λ
|
2.049
|
0.439
|
0.402
|
0.303
|
0.239
|
0.135
|
Contribution rate (%)
|
52.52
|
11.25
|
10.29
|
7.77
|
6.13
|
3.45
|
Accumulated contribution rate (%)
|
52.52
|
63.77
|
74.06
|
81.84
|
87.97
|
91.42
|
Ecological environmental vulnerability is an essential indicator to measure the level of regional ecological vulnerability. According to the extracted principal components, the formula for the ecological vulnerability index is as follows (Li et al. 2006):
![](data:image/png;base64,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)
where EVI is the ecological vulnerability index, Yi is the ith principal component, and ri is the corresponding contribution rate of the ith principal component. The calculation formula of the contribution rate is:
![](data:image/png;base64,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)
where ri is the corresponding contribution rate of the ith principal component, and λi is the eigenvalue of the ith principal component.
Overall, the larger is the ecological vulnerability index, the more fragile is the ecological environment and the worse is the system stability. In contrast, the smaller is the ecological vulnerability index, the higher is the stability of the ecosystem.
In order to solve the problem of comparability of ecological vulnerability assessment results in different years, and to analyze and measure them more clearly and intuitively, the EVI index is standardized, the calculation formula of which is as follows (Xu 2013):
![](data:image/png;base64,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)
where SVIi is the standardized value of the ecological vulnerability index in the ith year, and its variation range is 0-10, EVIi is the actual value of the ecological vulnerability index in the ith year, EVImax is the maximum of the ecological vulnerability index over many years, and EVImin is the minimum value of the ecological vulnerability index.
Ecological vulnerability classification
Table 4. Ecological vulnerability grading standard of Shennongjia.
Degree
|
Level
|
Standardized value
|
Characteristics of ecological vulnerability
|
Micro vulnerability
|
Ⅰ
|
< 2.0
|
The structure and function of the ecosystem are reasonable and complete, the ecosystem is stable, the ability of resisting external interference and self recovery is strong, and there is no ecological abnormality.
|
Mild vulnerability
|
Ⅱ
|
2.0-4.0
|
The structure and function of the ecosystem are relatively complete, the ecosystem is relatively stable, the ability to resist external interference and self recovery is strong, and there are potential ecological anomalies.
|
Moderate vulnerability
|
Ⅲ
|
4.0-6.0
|
The structure and function of the ecosystem can be maintained, the ecosystem is relatively unstable, it is sensitive to external interference, it possesses weak self-recovery ability, and there are a few ecological anomalies.
|
Severe vulnerability
|
Ⅳ
|
6.0-8.0
|
The structure and function of the ecosystem are defective, the ecosystem is unstable, it is sensitive to external interference, it is difficult to recover after damage, and there are many ecological anomalies.
|
Extreme
vulnerability
|
Ⅴ
|
≥ 8.0
|
The structure and function of the ecosystem are seriously degraded, the ecosystem is extremely unstable, it is extremely sensitive to external interference, and it is very difficult to recover after being damaged.
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According to the characteristics of the ecological environment in Shennongjia and related research results at home and abroad, the ecological vulnerability classification standard of Shennongjia was established. According to the differences of ecological vulnerability in the unit area, the study area was divided into five grades by using the equal difference classification method, which are: micro degree, mild degree, moderate degree, severe degree, and extreme vulnerability areas (Table 4). Based on the analysis of different levels of vulnerability and characteristics, this paper discusses the measures of ecological environment protection and the suitability scope of future national park development planning.
Regression fitting analysis
Taking the spatial data of ecological vulnerability index as the unit, the least square method was used to carry out linear regression analysis, and the slope of the fitting line was obtained to characterize the change trend of ecological vulnerability in the study period. The slope calculation formula is expressed as follows (Sun et al. 2010):
![](data:image/png;base64,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)
where K is the slope, n is the number of years, and EVIi is the ecological vulnerability index of the ith year. If the slope value is positive, the ecological vulnerability index increases, and the regional ecological vulnerability increases, if the slope value is negative, the ecological vulnerability index decreases, and the regional ecological vulnerability decreases.
Comprehensive ecological vulnerability index
In order to better express the quantitative characteristics of ecological vulnerability and determine the overall state of Shennongjia in the form of intuitive quantification, the comprehensive ecological vulnerability index (CEVI) was constructed to calculate the ecological vulnerability. The formula is given as follows:
![](data:image/png;base64,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)
where Li is the grade value of level i vulnerability, Ai is the area of level i vulnerability, and S is the total area of the study area.
Correlation and contribution analysis
As the number of patches (NP), largest patch index (LPI), aggregation index (AI), landscape division index (DIVISION) and Shannon diversity index (SHDI) are more sensitive to the change of landscape structure, and can fully reflect the fragmentation and diversity of regional landscape pattern, these five indexes are selected as the representative of the landscape pattern index (Zhang et al., 2016, Zhang et al., 2017). Coupling analysis with the ecological vulnerability index was conducted to identify the contribution of landscape pattern to vulnerability.
In multiple linear regression, if the dependent variable Y is linearly correlated with the independent variable Xi (i=1, 2, ……, k, k is the number of independent variables), the formula for calculating the sum of squares Pi of the partial regression of the independent variable Xi to Y is:
![](data:image/png;base64,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)
where u is the sum of the regression square of the whole model, Ui is the sum of the regression square of k-1 linear regression equation after Xi is excluded, and Pi is the sum of the partial regression square of Xi of each independent variable. Overall, the larger is the Pi value, the greater is the contribution of Xi to the regression square sum U. The formula for calculating the contribution rate is as follows:
![](data:image/png;base64,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)
where S is the contribution rate, and is the ratio of Pi to the cumulative value of all Pi.